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European Congress on Computational Methods in Applied ... - MGNet

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Craig C. Douglas and Karen M. WaltersREFERENCES[1] F. A. Bornemann and P. Deuflhard. The cascadic multigrid method for ellipticproblems. Numer. Math., 75:135–152, 1996.[2] F. A. Bornemann and R. Krause. Classical and cascadic multigrid - a methodicalcomparis<strong>on</strong>. In Proceed<strong>in</strong>gs of the N<strong>in</strong>th Internati<strong>on</strong>al C<strong>on</strong>ference <strong>on</strong> Doma<strong>in</strong>Decompositi<strong>on</strong>, pages 64–71, Bergen, Norway, 1998. Doma<strong>in</strong> Decompositi<strong>on</strong> Press.[3] D. Braess and W. Dahmen. A cascadic multigrid algorithm for the Stokes equati<strong>on</strong>.Numer. Math., 82:179–191, 1999.[4] L. Collatz. The Numerical Treatment of Differential Equati<strong>on</strong>s. Spr<strong>in</strong>ger-Verlag,Berl<strong>in</strong>, 1960.[5] P. Deuflhard, P. Le<strong>in</strong>en, and H. Yserentant. C<strong>on</strong>cepts of an adaptive hierarchicalf<strong>in</strong>ite element code. Impact Comput. Sci. Eng., 1:3–35, 1989.[6] J. M. Hyman. Mesh ref<strong>in</strong>ement and local <strong>in</strong>versi<strong>on</strong> of elliptic differential equati<strong>on</strong>s.J. Comput. Phys., 23:124–134, 1977.[7] V. V. Shaidurov. Some estimates of the rate of c<strong>on</strong>vergence for the cascadic c<strong>on</strong>jugategradientmethod. Comput. Math. Appl., 31:161–171, 1996.[8] Z. Shi and X. Xu. Cascadic multigrid method for parabolic problems. Prepr<strong>in</strong>t, 1999.[9] Z. Shi and X. Xu. Cascadic multigrid method for elliptic problems. East-West J.Numer. Math., 3:199–209, 1999.10

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